1. ## logarithms

An earthquake registers 6.1 on the richter scale. What is the rating on an earthquake that is twice as powerful?

2. The Richter Scale is log base 10.

So, an earthquake 2 times as powerful is the same as saying log2.

You're 1st earthquake is a 6.1.

So:

6.1 + log2 = your 2nd earthquake.

3. Hello, math123456!

An earthquake registers 6.1 on the Richter scale.
What is the rating on an earthquake that is twice as powerful?

The Richer scale is logarithmic.

If $X$ is the "power" of an earthquake, its Richter rating is: $\log(X)$

We have an earthquake with a Richter rating of 6.1.
If its power is $X$, we have: . $\log(X) \:=\:6.1$

An earthquake twice as power has power $2X$.

Its rating is: . $\log(2X) \;=\;\log(2) + \log(X) \:=\:0.30103 + 6.1 \;\approx\:6.4$

Curses . . . too slow ... again!
.